Analysis of pulsar timing data sets may provide the first direct detection of gravitational waves. This paper. the third in a series describing the mathematical framework implemented into the TEMPO2 pulsar timing Package, reports on using TEMPO2 to simulate the timing residuals induced by gravitational waves. The TEMPO2 simulations can be used to provide upper bounds on the amplitude of an isotropic, stochastic. gravitational wave background in our Galaxy and to determine the sensitivity of a given pulsar timing experiment to individual, supermassive, binary black hole systems.